برآورد ﺑُﻌﺪ ﻓﺮاﻛﺘﺎﻟﻲ ژئومورفولوژی کرانه‌های شمال خلیج فارس ﺑﺎ اﺳﺘﻔﺎده از روش ﺷﻤﺎرش ﺟﻌﺒﻪای

Estimate of costal geomorphology fractal dimension north of Persian Gulf by box – counting method
Abstract
From prospective of morphology, At first glance costal geomorphology is chaotic, intricate and complex. Geometrically fractal, estuaries have an internal order, and this order is so precise that the slightest irregularity can be obtained at any scale. In this study, fractal dimension in north of Persian Gulf shore for marine estuaries (Mouse’s estuary within the borders of Iran and Abd Allah’s estuary common border Kuwait and Iraq) and River meandering (Arvand roud River and Dalaki River in Iran North of Persian gulf) calculated by box-counting method. We used Arc GIS software and Landsat 8 of satellite image May 2016. In following, we make 10 partition scales from 100 KM to 100 M in each estuary and river of images. Our goal in this research is to investigate the pattern of order in the geometric geomorphological form of costal estuaries and Rivers meandering in the north of the Persian Gulf from a fractal point of view and its relationship to processes (geology, climate, hydraulic, etc.). Results show irregularity and disarrays in Mouse’s estuary by unit dimension fractal 1.5 to compare with Abd Allah’s estuary in Kuwait and Iraq by unit dimension fractal 0.67. Dimension fractal Arvand Roud River and Dalaki River are 0.53 and 0.46 respectively. In general, in this study, it can be concluded that geomorphological phenomena of fractal, the marine estuaries in the north of the Persian Gulf (especially Musa estuary) have entered the stage of turbulent edge. Also, on the 100-meter scale, fractal dimension of the Arvand Roud River is more turbulence than the Dalaki River. Geomorphological phenomena of estuaries and meanders at a scale of 100 meters are turbulent which shows the effectiveness of coastal and marine processes such as: tidal, marine waves, water erosion and loose sediments in estuaries and meanders in North of Persian gulf costal.
Introduction
The knowledge of geomorphology, which is based on the knowledge of forms (phenomena) and processes (forces), is quite complex, altering and difficult to predict. Costal and rivers are controlled by hydraulics, wind, tectonic, physical, chemical, geological, etc. Also Due to the large role of parameters in them, they usually show unknown and chaotic behavior processes. Fractal geometry provides a mathematical model for some of the more complex shapes and components in nature, such as beaches, hills, tree bark, clouds, and so on. The fractal dimension is a useful feature for examining the texture of components, classified shapes, and graphical analysis in some disciplines. Every phenomenon in the world has order. Although there may be irregularities, there is an order at the heart of each irregularity that can be accessed with special tools and methods and find the pattern and order in it. Self-similarity is one of the essential attributes of fractal in nature that may be quantified by fractal dimension. Our goal in this research is to investigate the pattern of order in the geometric geomorphological form of costal estuaries and Rivers meandering in the north of the Persian Gulf from a fractal point of view and its relationship to processes (geology, marine, geomorphology, etc.).
Keywords: "Fractai" - "Persian Gulf" - “Estuary" - "Arvand roud River" - "Box counting".
Methodology
In this study, in order to achieve the fractal dimension of coastal and River tributaries in the northern part of the Persian Gulf, the Landsat satellite image of May 8, 2016 was used. Arc GIS software was used to create Husdoroff networks. Also the Fishnet option was used to create square networks or houses on the area. The following relationship was used to obtain the fractal dimension of the geomorphological phenomena of River and sea estuaries in the Persian Gulf:
Nn=C/(R_n^D )

Nn= is the number of variables available for a phenomenon, C= is the constant coefficient, Rn= is the dimension of a special linear coefficient, and D= is the fractal dimension.
Results and discussion
Khowr Mousa
These results indicate the presence of three stages of foreground, threshold and threshold stage. The threshold and anomaly stages start from scales of 20 and 1.5 * 1, respectively, with a fractional fraction of 0.65 and 0.46. The total fractal regression for all three comprehensive backgrounds, thresholds, and anomalies is about 1.5. Also Khowr Mousa is 24% bigger than Khowr Abdullah.

Khowr Abdullah
Khor Abdullah is located in Kuwait and Iraq. According to Abdullah, the threshold and anomaly communities on scales 5 and 1.5 * 1 begin with a fractional fraction of 0.76 and 0.43, respectively. The total fractal for the whole population includes, foreground, threshold and anomaly of about 0.677.
Dalaki River
At the Dalaki River, the Astana and Anomaly communities begin at scales of 5 and 1.5 * 1 with a fractional fraction of 0.41 and 0.6, respectively. The overall fractal dimension of the Dalaki River is 0.46.
Arvand Roud River
The Arvand River has three main communities or stages, the anomaly of which is very small, and the background community and its threshold are endurance. The overall fractal dimension of the Arvand River is 0.5305.
Conclusion
The study's findings show that Mousa's marine estuary with a total fractal size of 1.5 is more disturbing than Abdullah's marine estuary with a fractal size of 0.67, which could indicate that Abdullah's marine estuary is younger than Musa's estuary. Conclusion this study shows that the estuaries north of the Persian Gulf are controlled by the operation of water power processes such as tidal, waves and sediment erosion and Tectonic forces have no role in creating and controlling estuaries directly. In general, Khor Mousa tends to be more chaotic than Khor Abdullah and Arvand roud River meanders desire to be more chaotic than Dalaki River from point of wives fractal dimension. Geometrically fractal, rivers controlled by costal and marine process and erosion sediment.
Keywords: "Fractai" - "Persian Gulf" - “Estuary" - "Arvand roud River" - "Box counting".